Retarded action principle and self-financing portfolio dynamics

TL;DR

This paper introduces the retarded action principle to model causality in the dynamics of self-financing portfolios, providing a differential framework applicable to various hedging strategies and exemplified through vanilla and storage options.

Contribution

It presents a novel differential representation based on the retarded action principle, enhancing understanding of causality in portfolio evolution.

Findings

Retarded action principle effectively models causality in portfolio dynamics.

Differential representation applicable to multiple hedging strategies.

Illustrations with vanilla and storage options demonstrate practical utility.

Abstract

We derive a consistent differential representation for the dynamics of a self-financing portfolio for different hedging strategies. In the basis of the derivation there is the so called "retarded action principle", which represents the causality in the evolution of dependent stochastic variables. We demonstrate this principle on example of a vanilla and a storage option.